Prepayment Analysis

The convention is to estimate CPR using the prepayment standard developed by the Public Securities Association, or PSA, the domestic bond market trade association now named the Bond Market Association. 

The PSA benchmark—100 percent PSA—assumes a starting prepayment rate of 0.2 percent. This increases by 0.2 points each month 

Assume that the constant monthly prepayment rate for a pool of mortgages is 2 percent, the outstanding principal balance at the start of the month is 72,200, and the scheduled principal payment is 223. To estimate the amount of principal prepayment for that month, the scheduled payment is subtracted from the balance, giving a total of 71,977, which is multiplied by the constant monthly prepayment rate, giving a prepayment amount for that month of 1,439. 

FIGURE 15.3 Ratio of Interest to Principal Payments for a Mortpape Pass-Through Security with 0 Percent CPR 

When the CPR is greater than zero, as in the 100 percent PSA and 200 percent PSA models, the principal payments will increase during 

---

An investor acquiring a pool of mortgt es from a lender measures the amount of associated prepayment risk by using a financial model to project the level of expected future payments. Although it is impossible to evaluate with any accuracy the prepayment potential of an individual mortgage, such analysis is reasonable for a large pool of loans. This is similar to what actuaries do when they assess the future liability of an insurer that has written personal pension contracts. The level of prepayment risk for a pool of loans is lower than that for an individual mortgt e. 

Because OAS analysis takes into account a mortgage-backed bond s option feature, it is less affected by a change in interest rates or the yield curve, which affect prepayments, than the bond s yield spread. Assuming a flat yield curve, the relationship between the OAS and the yield spread is expressed in equation (14.18). 

This chapter examines a number of issues relevant to participants in the fixed-income markets. The analysis presented is based on government-bond trading and is confined to generic bonds that are default-free, with no consideration given to factors that apply to corporate bonds, asset- and mortgage-backed bonds, convertibles, or other nonvanilla securities, or to issues such as credit risk and prepayment risk. Nevertheless, the principles adduced are pertinent to all relative-value fixed-income analysis. 

Thus the OAS is an indication of the value of the option element of the hond as well as the premium required by investors in return for accepting the default risk of the corporate bond. When OAS is measured as a spread between two bonds of similar default risk, the yield difference between the bonds reflects the value of the option element only. This is rare and the market convention is measure OAS over the equivalent benchmark government bond. OAS is used in the analysis of corporate bonds that incorporate call or put provisions, as well as mortgage-backed securities with prepayment risk. For both applications, the spread is calculated as the number of basis points over the yield of the government bond that would equate the price of both bonds. 

---